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First‐order undefinability of the notion of transfinitely uplifting cardinals
Author(s) -
Fujimoto Kentaro
Publication year - 2021
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201800050
Subject(s) - mathematics , order (exchange) , set (abstract data type) , order type , calculus (dental) , discrete mathematics , computer science , finance , economics , medicine , dentistry , programming language
Audrito and Viale introduced the new large cardinal notion of an (α)‐uplifting cardinal (for an ordinal α). We shall show that this notion cannot be defined (or expressed) in the standard first‐order language of set theory for every tranfinite α.